Variable Selection in High-Dimensional Varying Coefficient Models

• Activity Number: 380
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Lan Xue and Annie Qu*+
• Companies: Oregon State University and University of Illinois at Urbana-Champaign
• Keywords: difference convex programming ; L_0-regularization ; large-p small-n ; nonparametric function ; oracle property

Abstract

The varying coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. Here the response variables depend on covariates through linear regression, but the regression coefficients can vary and are modeled as a nonparametric function of other predictors. It is important to identify significant covariates associated with response variables, especially for high dimension setting where the number of covariates can be larger than the sample size, but the number of signal terms is relatively smaller than the sample size. We consider model selection in such setting and adopt difference convex programming to approximate the L0 penalty, and investigate global optimality properties of the varying coefficient estimator. The challenge of the variable selection problem here is that the dimension of the nonparametric form for the varying coefficient modeling could be infinite, in addition to dealing with the high-dimensional linear covariates. We show that the proposed varying coefficient estimator is consistent, enjoys the oracle property and achieves an optimal convergence rate for the non-zero nonparametric components for high-dimensional data. Our